JEE MainPhysicsModerateMechanical Properties of Fluids

Water flows in a horizontal tube (see figure). The pressure of
water changes by 700 Nm-2 between A and B where the area of cross
section are [IMAGE] and [IMAGE], respectively. Find the rate of flow of water
through the tube. (density of water [IMAGE] )

Show answer and solution

using equation of continuity

40V_{A} = 20V_{B}

\Rightarrow 2V_{A} = V_{B}

Using Bernoulli's equation

P_{A} + \frac{1}{2}\rho V_{A}^{2} = P_{B} + \frac{1}{2}\rho V_{B}^{2}

\Rightarrow P_{A} - P_{B} = \frac{1}{2}\rho\left( V_{B}^{2} - V_{A}^{2} \right)

\Rightarrow \Delta P = \frac{1}{2}1000\left( V_{B}^{2} - \frac{V_{B}^{2}}{4} \right)

\Rightarrow \Delta P = 500 \times \frac{3V_{B}^{2}}{4}

\Rightarrow V_{B} = \sqrt{\frac{(\Delta P) \times 4}{1500}} = \sqrt{\frac{(700) \times 4}{1500}m/s}

Volume flow rate

= 20 \times 100 \times V_{B} = 2732{cm}^{3}/s

Source: Grass-G / P-24 Physcis Paper 31 Dec.docx

Need a video for this idea?

Scan any doubt from your notes and get a whiteboard explanation.